Question

One of the angles of a triangle is $50°$. The other two angles are in the ratio $6:7$. The measure of the greatest angle is$\_\_\_\_\_$

Answer 1

Given

One of the angles of a triangle is $50°$

Let the other two angles be $6xand7x$

$\because$ The sum of all angles in a triangle is $180°$

$$\begin{gathered} 50+6x+7x=180 \\ \Rightarrow 50+13x=180 \\ \Rightarrow 13x=180-50 \\ \Rightarrow 13x=130 \\ \Rightarrow x=\frac{130}{13} \\ \Rightarrow x=10 \end{gathered}$$

the other two angles are

$$\begin{gathered} 6x=6\times 10=60° \\ 7x=7\times 10=70° \end{gathered}$$

so, the angles are $50°,60°and70°$

Hence, the measure of the greatest angle is $70°$